The ICC asserts jurisdictions over nationals of state parties, but also over acts that take place within the borders of state parties, regardless whether the actor is a national of a state party. The latter is the basis for the ICC's asserted jurisdiction against Benjamin Netanyahu and Yoav Gallant. Israel isn't a state party, but Palestine is, and the indictments were for conduct happening in Palestine. (The ICC also indicted a Hamas commander, which is more straightforward since he was a national of a party state).
So the fact that the US isn't a party to the Rome Statute doesn't necessarily bar the ICC from asserting jurisdiction. But.... Iran is not a state party, either. So I'm not sure how you get ICC jurisdiction against anybody on either side of the war.
Incidentally, Venezuela is a state party to the ICC. I'm no expert but between the boat strikes and Maduro kidnapping there is probably something actionable there against the President and other administration officials. But like you say, this is pretty academic given the infamous
Hague Invasion Act.